Analytical solutions for elastostatic problems of particle-and fiber-reinforced composites with inhomogeneous interphases

Abstract

By transforming the governing equations for displacement components into Riccati equations, analytical solutions for displacements, strains and stresses for Representive Volume Elements (RVEs) of particle- and fiber-reinforced composites containing inhomogenous interphases were obtained. The analytical solutions derived here are new and general for power-law variations of the elastic moduli of the inhomogeneous interphases. Given a power exponent, analytical expressions for the bulk moduli of the composites with inhomogenous interphases can be obtained. By changing the power exponent and the coefficients of the power terms, the solutions derived here can be applied to inhomogeneous interphases with many different property profiles. The results show that the modulus variation and the thickness of the inhomogeneous interphase have great effect on the bulk moduli of the composites. The particle will exhibit a sort of “size effect”, if there is an interphase.